A Markovian formalization of heart rate dynamics evinces a quantum-like hypothesis

Giuliani, Alessandro; Giudice, Pietro; Mancini, Anna Maria; Quatrini, Gianni; Pacifici, L; Webber, Charles L.; Zak, Michail; Zbilut, Joseph P.

doi:10.1007/bf00204206

Cited by 19 publications

(13 citation statements)

References 19 publications

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“…While this feature can be visually well appreciated, the inability to perform hypothesis testing can, however, lessen its usefulness. As a result, several variables have been suggested to quantify RP's and have found utility in a wide range of scientific explorations [6][7][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Recurrence quantification analysis and principal components in the detection of short complex signals

1998

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Recurrence plots were introduced to help aid the detection of signals in complicated data series. This effort was furthered by the quantification of recurrence plot elements. We now demonstrate the utility of combining recurrence quantification analysis with principal components analysis to allow for a probabilistic evaluation for the presence of deterministic signals in relatively short data lengths. PACS: 05.40 05.45, 07.05Rm, 07.05Kf

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Section: Introductionmentioning

confidence: 99%

Recurrence quantification analysis and principal components in the detection of short complex signals

1998

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“…For example, the existence of ‘modules’ implies some form of discretization occurs while any form of hierarchy implies the possibility to define ‘discrete layers’. The choice of the ‘optimal discretization’ when in presence of a sufficient amount of data can be based on the maximization of explained variance by a cluster analysis procedure [28], [29], a well studied statistical problem. A specific observation is assigned to its ‘discrete class’ on the basis the minimum distance to the k centroid values (average values for the studied variables, in this case the clustering variable is only one and corresponds to the expression level of the correspondent gene) relative to the best k-means cluster solution.…”

Section: Discussionmentioning

confidence: 99%

“…With sufficient data, using basic statistical analysis such as looking at standard deviation and mean values, we can appropriately discretize the state levels in both transcription factor binding activation and mRNA expression. In the case of a sufficiently high number of observations, a data driven discretization process can be performed by means of k-means cluster analysis [28], [29] by assigning each observation to the nearest cluster. The noise is not a major issue for this approach given that substituting actual value with the cluster centroid value (cluster = discrete classes) facilitates the noise filtration.…”

Section: Discussionmentioning

confidence: 99%

Sequential Logic Model Deciphers Dynamic Transcriptional Control of Gene Expressions

et al. 2007

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BackgroundCellular signaling involves a sequence of events from ligand binding to membrane receptors through transcription factors activation and the induction of mRNA expression. The transcriptional-regulatory system plays a pivotal role in the control of gene expression. A novel computational approach to the study of gene regulation circuits is presented here.MethodologyBased on the concept of finite state machine, which provides a discrete view of gene regulation, a novel sequential logic model (SLM) is developed to decipher control mechanisms of dynamic transcriptional regulation of gene expressions. The SLM technique is also used to systematically analyze the dynamic function of transcriptional inputs, the dependency and cooperativity, such as synergy effect, among the binding sites with respect to when, how much and how fast the gene of interest is expressed.Principal FindingsSLM is verified by a set of well studied expression data on endo16 of Strongylocentrotus purpuratus (sea urchin) during the embryonic midgut development. A dynamic regulatory mechanism for endo16 expression controlled by three binding sites, UI, R and Otx is identified and demonstrated to be consistent with experimental findings. Furthermore, we show that during transition from specification to differentiation in wild type endo16 expression profile, SLM reveals three binary activities are not sufficient to explain the transcriptional regulation of endo16 expression and additional activities of binding sites are required. Further analyses suggest detailed mechanism of R switch activity where indirect dependency occurs in between UI activity and R switch during specification to differentiation stage.Conclusions/SignificanceThe sequential logic formalism allows for a simplification of regulation network dynamics going from a continuous to a discrete representation of gene activation in time. In effect our SLM is non-parametric and model-independent, yet providing rich biological insight. The demonstration of the efficacy of this approach in endo16 is a promising step for further application of the proposed method.

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“…Simply stated, a terminal dynamic is a dynamic the reaches its terminus [25]. It comes to its end and simply stops.…”

Section: Partitioning the Cardiac Period As A Terminal Dynamicmentioning

confidence: 99%

Nonlinear Cardiac Dynamics

Webber¹

2012

Current Issues and Recent Advances in Pacemaker Therapy

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A Markovian formalization of heart rate dynamics evinces a quantum-like hypothesis

Cited by 19 publications

References 19 publications

Recurrence quantification analysis and principal components in the detection of short complex signals

Recurrence quantification analysis and principal components in the detection of short complex signals

Sequential Logic Model Deciphers Dynamic Transcriptional Control of Gene Expressions

Nonlinear Cardiac Dynamics

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